Lesson Plan

Approximate an irrational number by successively narrowing the interval between two rational bounds (e.g., showing that sqrt(2) is between 1.41 and 1.42 by squaring both endpoints)

Locate irrational numbers on a number line diagram to a specified degree of precision using rational approximations

Compare the size of two irrational numbers by computing rational approximations of each to enough decimal places to determine which is larger

Estimate the value of expressions involving irrational numbers (e.g., pi^2, 3sqrt(5)) by substituting rational approximations and computing

Explain why rational approximations of irrational numbers can be made arbitrarily close but never exact, and describe how to obtain a better approximation

8.NS.A.2

8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of sqrt(2), show that sqrt(2) is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.